If $(x + i y) (2 - 3 i) = 4 + i$ , then

x = - \frac{14}{3}, y = \frac{5}{13}

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x = \frac{5}{13}, y = \frac{14}{13}

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x = \frac{14}{13}, y = \frac{5}{13}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = \frac{5}{13}, y = - \frac{14}{13}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is A $x = \frac{5}{13}, y = \frac{14}{13}$
Given, $(x + i y) (2 - 3 i) = 4 + i$
$∴ x + i y = \frac{4 + i}{2 - 3 i}$
On rationalizing the denominator, we get
$(x + i y) = \frac{(4 + i) (2 + 3 i)}{13} = \frac{5 + 14 i}{13}$
$∴ x = \frac{5}{13}, y = \frac{14}{13}$

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If (x+iy)(2−3i)=4+i, then

The correct option is A x=513,y=1413Given, (x+iy)(2−3i)=4+i∴x+iy=4+i2−3iOn rationalizing the denominator, we get(x+iy)=(4+i)(2+3i)13=5+14i13∴x=513,y=1413

If $(x + i y) (2 - 3 i) = 4 + i$ , then

The correct option is A $x = \frac{5}{13}, y = \frac{14}{13}$
Given, $(x + i y) (2 - 3 i) = 4 + i$
$∴ x + i y = \frac{4 + i}{2 - 3 i}$
On rationalizing the denominator, we get
$(x + i y) = \frac{(4 + i) (2 + 3 i)}{13} = \frac{5 + 14 i}{13}$
$∴ x = \frac{5}{13}, y = \frac{14}{13}$